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- Title
The motion induced by a radially stretching membrane in a rotating fluid system.
- Authors
Weidman, Patrick D.
- Abstract
The flow induced above an impermeable sheet undergoing linear radial stretching in a system rotating at angular velocity Ω is investigated. The problem is governed by the single parameter σ = Ω/a, where a is the stretching rate of the membrane. A similarity reduction of the Navier-Stokes equations leads to a pair of nonlinearly-coupled ordinary differential equations which are numerically solved over the range 0 ≤ σ ≤ 10. Coriolis forces acting on the radially stretching flow in the vicinity of the wall induces azimuthal flow in the boundary layer. A large-σ analysis of the system leads to the Ekman equations describing the balance of Coriolis and viscous forces for which an exact solution is presented. Numerical results for the radial and azimuthal shear stresses, along with the magnitude of the velocity induced into the boundary layer, are shown to be in good agreement with the large-σ asymptotic results.
- Subjects
RADIAL stresses; RADIAL basis functions; ANGULAR velocity measurement; NUMERICAL solutions to differential equations; EKMAN motion theory; MATHEMATICAL models
- Publication
ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2015, Vol 95, Issue 12, p1582
- ISSN
0044-2267
- Publication type
Article
- DOI
10.1002/zamm.201500094